The versatile defender signed a three-year deal with the Los Rojiblancos.
The 28-year-old after completing his move to the Spanish capital becomes Atleti’s third defensive signing of the summer.
With the side losing their key prospects Diego Godin and Antoine Griezmann to Inter Milan and Barcelona respectively, Diego Simone’s side have recruited other players to garnish the squad.
Atletico Madrid have already signed Benfica’s wonderkid Joao Felix as they also made Chelsea’s loanee Alvaro Morata’s deal permanent, securing centre-back Felipe from Porto and left-back Renan Lodi from Brazilian side Athletico Paranaense.
Trippier's arrival brings Atletico's total transfer spend so far this summer to more than £170m having received £107.7 million after offloading France striker Antoine Griezmann to LaLiga champions Barcelona.
Trippier did not travel with the Spurs squad for their pre-season tour of Asia as he was made to finalise his move to Atletico Madrid.
The right full-back made his last appearance for Tottenham in the last season’s Champions League final against Liverpool in June.
Tottenham recruited Trippier from Burnley in June 2015 for a reported fee of £3.5 million as he featured more than 100 times for the Lily Whites.
Trippier made twenty-seven appearances with three assists and one goal for Tottenham in the 2018/19 Premier League season.
